Selective Filter System Based on Multi-Defectives Resonators Inserted in 1D Acoustic Periodic Star Waveguides

The spectre of acoustic wave transmission through a one-dimensional phononic comb-like structure is derived using the Green Function Method. The devised system comprises a finite series of cells, where each cell consists of a segment of length d1 connected at its end by resonators of lengths d2. The defective resonators are positioned at two distinct sites, each having lengths d02 and d03, which differ from those of the ideal resonators. The perfect phononic structure exhibits the presence of pass bands and band gaps where the propagation of acoustic waves is prohibited. To facilitate comparison, we initially introduce a single defect resonator situated at one site, thereby inducing two defect modes inside the band gaps. These defect modes exhibit noticeable transmissions and high-quality factors, enabling our proposed system to function as a single narrow selective filter. When introducing two defect resonators of varying lengths at different sites, multiple localized modes emerge in the band gaps. Consequently, the proposed system operates as highly narrow multichannel filters with the defect modes shifting towards lower frequencies as the lengths of the defect resonators increase. The obtained results underscore the dependency on the frequencies of defect modes, the lengths of defect resonators and their positions in the structure.